Cox Regression Workflow

Cox proportional hazards regression adjusts survival comparisons for covariates, producing Hazard Ratios (HR) with 95% CI. Licklider runs the proportional hazards assumption check via Schoenfeld residuals, discloses violations, and generates a forest plot of adjusted HRs — the standard for clinical survival reporting.

STEP 1 — The Scenario

Researcher Profile

An oncologist extending the KM analysis above by adjusting the treatment effect for key prognostic variables: age, ECOG performance status (0-1 vs. 2), and disease stage (III vs. IV).

Research Question

"What is the adjusted HR for treatment arm after controlling for age, performance status, and disease stage? Are any covariates independent prognostic factors?"

Dataset

Same 88 patients as the KM scenario
Additional columns: Age (continuous), ECOG_PS (binary: 0-1 vs. 2), Stage (binary: III vs. IV)
Outcome: OS_months (time), Event (1=death, 0=censored)

STEP 2 — Licklider Analysis Path

1. Data Upload & Model Specification

Licklider detects the time-to-event structure and the covariate columns. The researcher specifies: fixed predictors = Arm, Age, ECOG_PS, Stage. The Covariate Selection Audit (4.6.3) asks: "Were these covariates pre-specified in the protocol?"

2. Data Contract Declaration

Observation unit: one patient. Event: death. Analysis purpose: confirmatory (primary endpoint with pre-specified covariates).

3. Cox Model Fitting

Multivariable Cox PH model: Surv(OS_months, Event) ~ Arm + Age + ECOG_PS + Stage. For each predictor: HR, 95% CI (Wald), z-statistic, and p-value are reported. Concordance (C-statistic, equivalent to AUC for survival) is calculated.

4. Proportional Hazards Assumption Check

Licklider runs the Schoenfeld residuals test for each covariate. If the test is significant (p<0.05 for any predictor), the PH assumption is violated for that variable — meaning its effect changes over time. Licklider flags this and recommends:

Time-varying coefficient model for the offending variable, or
Stratification by the violating variable (if it is not the primary predictor of interest), or
Restricted mean survival time (RMST) as an alternative summary measure

5. Forest Plot

A forest plot is generated showing HR and 95% CI for all predictors. The reference category for each categorical variable is clearly labeled. The overall model C-statistic is annotated.

STEP 3 — Guards & Disclosures Activated

PH Assumption Check Disclosure

The Schoenfeld residuals test result (χ² and p for each covariate, and the global test) is always reported in the statistical output. If any covariate violates the PH assumption and the researcher proceeds without addressing it, a mandatory warning is included in the exported Methods text.

Covariate Selection Audit (4.6.3)

If covariates were selected based on univariate significance (stepwise selection), the analysis is labeled exploratory and the Methods text includes a disclosure that stepwise selection inflates Type I error rates.

Effect Size Reporting (4.1.2)

HR and 95% CI are required for every predictor in the forest plot. The C-statistic (model discrimination) is reported as the overall effect size measure. HR without CI is blocked from export.

Causal Language Detection (3.1.5)

The auto-generated text requires "was associated with" (not "caused" or "reduced mortality") for observational survival data. The causal language guard is active by default.

Multiple Comparison Compliance (4.1.5)

If multiple Cox models are fitted (e.g., testing different covariate combinations), the Analysis Family Ledger tracks the total number of models tested and requires a disclosure of the model selection strategy.

STEP 4 — Export Package

Figure: Forest plot — HR (95% CI) for all predictors — 300 dpi TIFF/PDF
Statistical Report: Full Cox model output (HR, 95% CI, z, p for all covariates); Schoenfeld residuals test (global and per-variable); C-statistic; concordance; event/censoring summary
Methods Text: "Multivariable Cox proportional hazards regression was used to assess the association of treatment arm with OS after adjustment for age, ECOG performance status, and disease stage. The proportional hazards assumption was verified using Schoenfeld residuals. Hazard ratios and 95% CIs are reported. C-statistic=[value]. n=88; events=62."
Figure Legend: HR interpretation (HR<1 = lower hazard in Arm A), CI method, C-statistic, n, events n, reference categories labeled
Preprocessing Audit Log: Covariate declaration date; PH check result; any time-varying covariate handling applied